A:When the apparatus of YDSE is brought in a liquid from air, the fringe width decreases.
R: The wavelength of light decreases in the liquid.

Options

A. IF both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark(2)
C. IF Assertion is true statement but Reason is false then mark(3)
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To solve the question regarding the assertion and reason related to Young's Double Slit Experiment (YDSE) when the apparatus is submerged in a liquid, we will analyze both statements step by step.

### Step 1: Understanding the Fringe Width Formula
The fringe width (β) in Young's Double Slit Experiment is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \lambda \) = wavelength of light,
- \( D \) = distance from the slits to the screen,
- \( d \) = separation between the slits.

### Step 2: Effect of Medium on Wavelength
When the apparatus is moved from air to a liquid, the wavelength of light changes. The new wavelength \( \lambda' \) in the liquid is given by:
\[ \lambda' = \frac{\lambda}{\mu} \]
where \( \mu \) is the refractive index of the liquid (which is greater than 1).

### Step 3: New Fringe Width in Liquid
Substituting the new wavelength into the fringe width formula gives:
\[ \beta' = \frac{\lambda' D}{d} = \frac{\left(\frac{\lambda}{\mu}\right) D}{d} = \frac{\lambda D}{\mu d} \]
This shows that the new fringe width \( \beta' \) is:
\[ \beta' = \frac{\beta}{\mu} \]
Since \( \mu > 1 \), it follows that \( \beta' < \beta \). Therefore, the fringe width decreases when the apparatus is submerged in the liquid.

### Step 4: Evaluating the Assertion and Reason
- **Assertion (A)**: When the apparatus of YDSE is brought in a liquid from air, the fringe width decreases. This statement is **true**.
- **Reason (R)**: The wavelength of light decreases in the liquid. This statement is also **true** because the wavelength decreases in a medium with a refractive index greater than 1.

### Step 5: Conclusion
Since both the assertion and reason are true, and the reason correctly explains the assertion, the correct answer is that both statements are true and the reason explains the assertion.

### Final Answer:
Both the assertion and reason are true, and the reason correctly explains the assertion.

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